Complexity in Human and Humanoid Biomechanics

We propose the following complexity conjecture: in a combined biomechanical system, where the action of Newtonian laws cannot be neglected, it is the mechanical part that determines the lower limit of complexity of the combined system, commonly defined as the number of mechanical degrees of freedom. The biological part of such a system, being "more intelligent", naturally serves as a "controller" for the "nonintelligent" mechanical "plant". Although, in some special cases, the behavior of the combined system might have a "simple" output, a realistic internal state space analysis shows that the total system complexity represents either the superposition, or a kind of "macroscopic entanglement" of the two partial complexities. Neither "mutual canceling" nor "averaging" of the mechanical degrees of freedom generally occurs in such a biomechanical system. The combined system has both dynamical and control complexities. The "realistic" computational model of such a system also has its own computational complexity. We demonstrate the validity of the above conjecture using the example of the physiologically realistic computer model. We further argue that human motion is the simplest well-defined example of a general human behavior, and discuss issues of simplicity versus predictability/controllability in complex systems. Further, we discuss self-assembly in relation to conditioned training in human/humanoid motion. It is argued that there is a significant difference in the observational resolution of human motion while one is watching "subtle" movements of a human hands playing a piano versus "coarse" movements of a human crowd at a football stadium from an orbital satellite. Techniques such as cellular automata can model the coarse crowd motion, but not the subtle hierarchical neural control of the dynamics of human hands playing a piano. Therefore, we propose the observational resolution as a new measure of biomechanical complexity. Finally, there is a possible route to apparent simplicity in biomechanics, in the form of oscillatory synchronization, both external (kinematical) and internal (control).